To install OpenTTD, you should drag the game to any location you want and in that folder, you should create a folder called "data". It should contain:
sample.cat
trg1r.grf
trgcr.grf
trghr.grf
trgir.grf
trgtr.grf

(Alternatively you can use the TTD GRF files from the DOS version: TRG1.GRF, TRGC.GRF, TRGH.GRF, TRGI.GRF, TRGT.GRF. A few minor graphical glitches with the DOS graphics remain. E.g. the autorail button in the rail toolbar doesn't look as nice as with the Windows graphics.)

You should also use the data folder to add any custom grf files if you like

if you want music, you can add a GM folder and add all .gm files from TTD inside it

If you want to use the scenarios, you can copy the scenario folder as well. If you already have one, just copy the content so you don't overwrite old ones that have been removed.

In the end, you should have a folder containing:
OpenTTD (the actual game)
data (containing the grf files)
GM   (optional for music)
scenario (optional pregenerated maps)

The game adds some items by itself when it runs, like a save folder and a setting file